# Orthomodular lattices can be converted into left residuated l-groupoids

@article{Chajda2017OrthomodularLC,
title={Orthomodular lattices can be converted into left residuated l-groupoids},
author={Ivan Chajda and Helmut Langer},
journal={Miskolc Mathematical Notes},
year={2017},
volume={18},
pages={685}
}
• Published 28 September 2018
• Mathematics
• Miskolc Mathematical Notes
We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional conditions expressed in the language of residuated structures. Also conversely, every left residuated l-groupoid satisfying the mentioned conditions can be organized into an orthomodular lattice.
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